### Theory:

A solution of an equation is a number substituted for an unknown variable which makes the equality in the equation true.
In a two-variable equation, the solution also contains two values.
Method I
Consider an equation with two variable $$x + 2y = 20$$.

We need to substitute values for $$x$$ and $$y$$ in $$LHS$$, which should satisfy the equation and give the result value as $$RHS$$.

Let us substitute $$x = 2$$ and $$y = 9$$.

$$LHS = x + 2y$$

$$= 2 + 2(9)$$

$$= 20 = RHS$$

So, $$x = 2$$ and $$y = 9$$ satisfy the given equation, which is the solution of the given equation.

Therefore, the solution can be written as $$(2, 9)$$.
Is there only one solution available for the single linear equation in two variables?

No, we can find many solutions for the single linear equation in two variables.
Substitute $$x = 10$$ and $$y = 5$$.

$$LHS = x + 2y$$

$$= 10 + 2(5)$$

$$= 20 = RHS$$

So, $$(10, 5)$$ is also a solution to the given equation.

Important!
We can find many solutions for a single equation with two variables.
Method II
Steps to find a solution of equation:
1. Substitute $$x = 0$$ and $$y = 0$$ in the given equation.

2. Next, perform an arithmetic operation to find the value of $$x$$ and $$y$$, which are the solutions of  the given equation.
Consider the same equation: $$x + 2y = 20$$

Substitute $$x = 0$$ in the given equation.

$$0 + 2y = 20$$

$$2y = 20$$

$y=\frac{20}{2}$

$$y = 10$$

Thus, $$(0, 10)$$ is one solution of the given equation.

Similarly, substitute $$y = 0$$ in the given equation.

$$x + 2(0) = 20$$

$$x + 0 = 20$$

$$x = 20$$

Thus, $$(20, 0)$$ is another solution to the given equation.

Important!
The solution of a linear equation is not affected when:

(i) the same number is added to (or subtracted from) both sides of the equation.

(ii) you multiply or divide both sides of the equation by the same non-zero number.